Warning: Even though FGb can be downloaded directly form this Web page it is strongly recommended to download the SALSA library. In addition to Gröbner bases, SALSA Software contains recent algorithms for computing certified solutions of systems of polynomial equalities, inequalities and inequations.

Gb is a program (90 000 lines of C++) for computing Grobner bases, implement "standard" algoritms:

1. Buchberger and numerous variant/improvements
2. FGLM algorithm
3. Lextriangular algorithm
4. Hilbert functions
5. Hilbert driven algorithms
6. Different Ground rings:
   1. Big integer
   2. Coefficient modulo p (several implementations)
   3. Complex numbers
   4. Hybrid arithmetics

FGb is a rather small but very efficient program written in C for solving polynomial systems:

1. F4 for computing Groebner bases
2. F5 removing Buchberger criteria (in test)
3. F7 decomposition into primes
4. F2 fast change of ordering
5. Different Ground fields:
   1. Rationals
   2. Modulo p
   3. Finite Fields
   4. Complex numbers
   5. Hybrid arithmetics
   6. Free parameters (currently only one)